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Hemifamity family: Difference between revisions

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m Cleanup (2/2)
Line 6: Line 6:
[[Comma list]] c = 5120/5103
[[Comma list]] c = 5120/5103


[[Mapping]]: [<1 0 0 10|, <0 1 0 -6|, <0 0 1 1|]
[[Mapping]]: [{{val| 1 0 0 10 }}, {{val| 0 1 0 -6 }}, {{val| 0 0 1 1 }}]


Mapping generators: ~2, ~3, ~5
Mapping generators: ~2, ~3, ~5


Map to lattice: [<0 1 2 -4|, <0 0 1 1|]
Map to lattice: [{{val| 0 1 2 -4 }}, {{val| 0 0 1 1 }}]


Lattice basis:  
Lattice basis:  
Line 18: Line 18:
[[Minimax tuning]]:
[[Minimax tuning]]:
* [[7-odd-limit]]: 3 and 7 1/7c sharp, 5 just
* [[7-odd-limit]]: 3 and 7 1/7c sharp, 5 just
: [|1 0 0 0>, |10/7 1/7 1/7 -1/7>, |0 0 1 0>, |10/7 -6/7 1/7 6/7>]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 1/7 1/7 -1/7 }}, {{monzo| 0 0 1 0 }}, {{monzo| 10/7 -6/7 1/7 6/7 }}]
: [[Eigenmonzo]]s: 2, 5/4, 7/6
: [[Eigenmonzo]]s: 2, 5/4, 7/6
* [[9-odd-limit]]: 3 1/8c sharp, 5 just, 7 1/4c sharp
* [[9-odd-limit]]: 3 1/8c sharp, 5 just, 7 1/4c sharp
: [|1 0 0 0>, |5/4 1/4 1/8 -1/8>, |0 0 1 0>, |5/2 -3/2 1/4 3/4>]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/4 1/4 1/8 -1/8 }}, {{monzo| 0 0 1 0 }}, {{monzo| 5/2 -3/2 1/4 3/4 }}]
: [[Eigenmonzo]]s: 2, 5/4, 9/7
: [[Eigenmonzo]]s: 2, 5/4, 9/7


Line 42: Line 42:
[[Comma list]]: 441/440, 896/891
[[Comma list]]: 441/440, 896/891


[[Mapping]]: [<1 0 0 10 17|, <0 1 0 -6 -10|, <0 0 1 1 1|]
[[Mapping]]: [{{val| 1 0 0 10 17 }}, {{val| 0 1 0 -6 -10 }}, {{val| 0 0 1 1 1 }}]


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[11-odd-limit]]
* [[11-odd-limit]]
: [|1 0 0 0 0>, |17/10 0 1/10 0 -1/10>, |17/5 -2 6/5 0 -1/5>, |16/5 -2 3/5 0 2/5>, |17/5 -2 1/5 0 4/5>]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 17/10 0 1/10 0 -1/10 }}, {{monzo| 17/5 -2 6/5 0 -1/5 }}, {{monzo| 16/5 -2 3/5 0 2/5 }}, {{monzo| 17/5 -2 1/5 0 4/5 }}]
: [[Eigenmonzo]]s: 2, 10/9, 11/9
: [[Eigenmonzo]]s: 2, 10/9, 11/9


Map to lattice: [<0 1 4 -2 -6|, <0 0 -1 -1 -1|]
Map to lattice: [{{val| 0 1 4 -2 -6 }}, {{val| 0 0 -1 -1 -1 }}]


Lattice basis:  
Lattice basis:  
Line 66: Line 66:
Comma list: 196/195, 352/351, 364/363
Comma list: 196/195, 352/351, 364/363


Mapping: [<1 0 0 10 17 22|, <0 1 0 -6 -10 -13|, <0 0 1 1 1 1|]
Mapping: [{{val| 1 0 0 10 17 22 }}, {{val| 0 1 0 -6 -10 -13 }}, {{val| 0 0 1 1 1 1 }}]


Minimax tuning:  
Minimax tuning:  
* 13-odd-limit
* 13-odd-limit eigenmonzos: 2, 10/9, 13/10
: Eigenmonzos: 2, 10/9, 13/10
* 15-odd-limit eigenmonzos: 2, 15/13, 6/5
* 15-odd-limit
: Eigenmonzos: 2, 15/13, 6/5


Vals: {{Val list| 29, 41, 46, 58, 87, 145, 232, 377cef }}
Vals: {{Val list| 29, 41, 46, 58, 87, 145, 232, 377cef }}
Line 83: Line 81:
[[Comma list]]: 540/539, 5120/5103
[[Comma list]]: 540/539, 5120/5103


[[Mapping]]: [<1 0 0 10 -18|, <0 1 0 -6 15|, <0 0 1 1 -1|]
[[Mapping]]: [{{val| 1 0 0 10 -18 }}, {{val| 0 1 0 -6 15 }}, {{val| 0 0 1 1 -1 }}]


[[Minimax tuning]]
[[Minimax tuning]]
: [|1 0 0 0 0>, |4/3 0 2/21 -1/21 1/21>, |0 0 1 0 0>, |2 0 3/7 2/7 -2/7>, |2 0 3/7 -5/7 5/7>]
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 4/3 0 2/21 -1/21 1/21 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 2 0 3/7 2/7 -2/7 }}, {{monzo| 2 0 3/7 -5/7 5/7 }}]
: [[Eigenmonzo]]s: 2, 5/4, 14/11
: [[Eigenmonzo]]s: 2, 5/4, 14/11
{{Val list|legend=1| 41, 53, 58, 94, 99e, 111, 152, 555de, 707de, 859bde }}


Projection pairs: 5120/729 11 14348907/1310720
Projection pairs: 5120/729 11 14348907/1310720
{{Val list|legend=1| 41, 53, 58, 94, 99e, 111, 152, 555de, 707de, 859bde }}


== 13-limit ==
== 13-limit ==
Line 100: Line 99:
Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit
* 13- and 15-odd-limit
: [|1 0 0 0 0 0>, |13/8 -1/2 1/8 0 0 1/8>, |13/4 -3 5/4 0 0 1/4>, |7/2 0 1/2 0 0 -1/2>, |25/8 -9/2 5/8 0 0 13/8>, |13/4 -3 1/4 0 0 5/4>]
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 13/8 -1/2 1/8 0 0 1/8 }}, {{monzo| 13/4 -3 5/4 0 0 1/4 }}, {{monzo| 7/2 0 1/2 0 0 -1/2 }}, {{monzo| 25/8 -9/2 5/8 0 0 13/8 }}, {{monzo| 13/4 -3 1/4 0 0 5/4 }}]
: [[Eigenmonzo]]s: 2, 11/8, 14/13
: [[Eigenmonzo]]s: 2, 11/8, 14/13


Line 108: Line 107:
Comma list: 352/351, 540/539, 847/845, 442/441
Comma list: 352/351, 540/539, 847/845, 442/441


Mapping: [<1 0 0 10 -18 -13 32|, <0 1 0 -6 15 12 -22|, <0 0 1 1 -1 -1 3|]
Mapping: [{{val| 1 0 0 10 -18 -13 32 }}, {{val| 0 1 0 -6 15 12 -22 }}, {{val| 0 0 1 1 -1 -1 3 }}]


Minimax tuning:  
Minimax tuning:  
* 17-odd-limit
* 17-odd-limit
: [|1 0 0 0 0 0 0>, |13/12 0 0 1/12 1/6 -1/12 0>, |-7/4 0 0 5/4 3/2 -5/4 0>, |7/4 0 0 3/4 1/2 -3/4 0>, |0 0 0 0 1 0 0>, |7/4 0 0 -1/4 1/2 1/4 0>, |35/12 0 0 23/12 5/6 -23/12 0>]
: [{{monzo| 1 0 0 0 0 0 0 }}, {{monzo| 13/12 0 0 1/12 1/6 -1/12 0 }}, {{monzo| -7/4 0 0 5/4 3/2 -5/4 0 }}, {{monzo| 7/4 0 0 3/4 1/2 -3/4 0 }}, {{monzo| 0 0 0 0 1 0 0 }}, {{monzo| 7/4 0 0 -1/4 1/2 1/4 0 }}, {{monzo| 35/12 0 0 23/12 5/6 -23/12 0 }}]
: [[Eigenmonzo]]s: 2, 11/8, 14/13
: [[Eigenmonzo]]s: 2, 11/8, 14/13


Line 122: Line 121:
[[Comma list]]: 385/384, 2200/2187
[[Comma list]]: 385/384, 2200/2187


[[Mapping]]: [<1 0 0 10 -3|, <0 1 0 -6 7|, <0 0 1 1 -2|]
[[Mapping]]: [{{val| 1 0 0 10 -3 }}, {{val| 0 1 0 -6 7 }}, {{val| 0 0 1 1 -2 }}]


Mapping generators: ~2, ~3, ~5
Mapping generators: ~2, ~3, ~5
Line 128: Line 127:
[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[11-odd-limit]]
* [[11-odd-limit]]
: [|1 0 0 0 0>, |5/3 0 1/6 -1/6 0>, |26/9 0 13/18 -7/18 -1/3>, |26/9 0 -5/18 11/18 -1/3>, |26/9 0 -5/18 -7/18 2/3>]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 0 }}, {{monzo| 26/9 0 13/18 -7/18 -1/3>, {{monzo| 26/9 0 -5/18 11/18 -1/3 }}, {{monzo| 26/9 0 -5/18 -7/18 2/3 }}]
: [[Eigenmonzo]]s: ~2, ~14/11, ~7/5
: [[Eigenmonzo]]s: ~2, ~14/11, ~7/5


Line 140: Line 139:
Comma list: 325/324, 352/351, 385/384
Comma list: 325/324, 352/351, 385/384


Mapping: [<1 0 0 10 -3 2|, <0 1 0 -6 7 4|, <0 0 1 1 -2 -2|]
Mapping: [{{val| 1 0 0 10 -3 2 }}, {{val| 0 1 0 -6 7 4 }}, {{val| 0 0 1 1 -2 -2 }}]


Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit
* 13- and 15-odd-limit
: [|1 0 0 0 0 0>, |5/3 0 1/6 -1/6 0 0>, |26/9 0 13/18 -7/18 -1/3 0>, |26/9 0 -5/18 11/18 -1/3 0>, |26/9 0 -5/18 -7/18 2/3 0>, |26/9 0 -7/9 1/9 2/3 0>]
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 0 0 }}, {{monzo| 26/9 0 13/18 -7/18 -1/3 0 }}, {{monzo| 26/9 0 -5/18 11/18 -1/3 0 }}, {{monzo| 26/9 0 -5/18 -7/18 2/3 0 }}, {{monzo| 26/9 0 -7/9 1/9 2/3 0 }}]
: Eigenmonzos: 2, 14/11, 7/5
: Eigenmonzos: 2, 14/11, 7/5


Line 151: Line 150:
: Angle (3/2, 27/20) = 80.5628 degrees
: Angle (3/2, 27/20) = 80.5628 degrees


Map to lattice: [<0 1 3 -3 1 -2|, <0 0 -1 -1 2 2|]
Map to lattice: [{{val| 0 1 3 -3 1 -2 }}, {{val| 0 0 -1 -1 2 2 }}]


Vals: {{Val list| 7, 41, 46, 53, 87, 94, 140, 181, 321, 408 }}
Vals: {{Val list| 7, 41, 46, 53, 87, 94, 140, 181, 321, 408 }}
Line 164: Line 163:
[[Comma list]]: 3025/3024, 5120/5103
[[Comma list]]: 3025/3024, 5120/5103


[[Mapping]]: [<1 0 0 10 7|, <0 1 1 -5 -2|, <0 0 2 2 -1|]
[[Mapping]]: [{{val| 1 0 0 10 7 }}, {{val| 0 1 1 -5 -2 }}, {{val| 0 0 2 2 -1 }}]


Mapping generators: ~2, ~3, ~128/99
Mapping generators: ~2, ~3, ~128/99
Line 170: Line 169:
[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[11-odd-limit]]:  
* [[11-odd-limit]]:  
: [|1 0 0 0 0>, |8/5 2/5 0 -1/15 -2/15>, |14/5 6/5 0 7/15 -16/15>, |16/5 -6/5 0 13/15 -4/15>, |16/5 -6/5 0 -2/15 11/15>]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 8/5 2/5 0 -1/15 -2/15 }}, {{monzo| 14/5 6/5 0 7/15 -16/15 }}, {{monzo| 16/5 -6/5 0 13/15 -4/15 }}, {{monzo| 16/5 -6/5 0 -2/15 11/15 }}]
: [[Eigenmonzo]]s: 2, 11/9, 9/7
: [[Eigenmonzo]]s: 2, 11/9, 9/7


Vals: {{Val list| 41, 87, 111, 152, 198, 239, 350, 391, 478, 589 }}
{{Val list|legend=1| 41, 87, 111, 152, 198, 239, 350, 391, 478, 589 }}


[[Badness]]: 0.994 × 10<sup>-3</sup>
[[Badness]]: 0.994 × 10<sup>-3</sup>
Line 182: Line 181:
[[Comma list]]: 176/175, 5120/5103
[[Comma list]]: 176/175, 5120/5103


[[Mapping]]: [&lt;1 0 0 10 6|, &lt;0 1 0 -6 -6|, &lt;0 0 1 1 3|]
[[Mapping]]: [{{val| 1 0 0 10 6 }}, {{val| 0 1 0 -6 -6 }}, {{val| 0 0 1 1 3 }}]


{{Val list|legend=1| 7, 12, 39, 46, 53, 58, 99, 111 }}
{{Val list|legend=1| 7, 12, 39, 46, 53, 58, 99, 111 }}
Line 193: Line 192:
[[Comma list]]: 3388/3375, 5120/5103
[[Comma list]]: 3388/3375, 5120/5103


[[Mapping]]: [&lt;1 0 0 10 -6|, &lt;0 2 0 -12 9|, &lt;0 0 1 1 1|]
[[Mapping]]: [{{val| 1 0 0 10 -6 }}, {{val| 0 2 0 -12 9 }}, {{val| 0 0 1 1 1 }}]


{{Val list|legend=1| 29, 53, 58, 87, 111, 140, 198 }}
{{Val list|legend=1| 29, 53, 58, 87, 111, 140, 198 }}
Line 204: Line 203:
Comma list: 352/351, 676/675, 847/845
Comma list: 352/351, 676/675, 847/845


Mapping: [&lt;1 0 0 10 -6 -1|, &lt;0 2 0 -12 9 3|, &lt;0 0 1 1 1 1|]
Mapping: [{{val| 1 0 0 10 -6 -1 }}, {{val| 0 2 0 -12 9 3 }}, {{val| 0 0 1 1 1 1 }}]


Vals: {{Val list| 29, 53, 58, 87, 111, 140, 198 }}
Vals: {{Val list| 29, 53, 58, 87, 111, 140, 198 }}
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